In [3]: 
import sys
sys.setrecursionlimit(10000)
import warnings
warnings.filterwarnings('ignore', category=DeprecationWarning)
In [2]: 
import cPickle
import gzip

from breze.learn.data import one_hot
from breze.learn.base import cast_array_to_local_type
from breze.learn.utils import tile_raster_images

import climin.stops
import climin.initialize

from breze.learn import hvi
from breze.learn.hvi import HmcViModel
from breze.learn.hvi.energies import (NormalGaussKinEnergyMixin, DiagGaussKinEnergyMixin)
from breze.learn.hvi.inversemodels import MlpGaussInvModelMixin

from matplotlib import pyplot as plt
from matplotlib import cm

import numpy as np

#import fasttsne

from IPython.html import widgets
%matplotlib inline

import theano
theano.config.compute_test_value = 'ignore'#'raise'
from theano import (tensor as T, clone)

C:\Anaconda\lib\site-packages\scipy\lib\_util.py:35: DeprecationWarning: Module scipy.linalg.blas.fblas is deprecated, use scipy.linalg.blas instead
  DeprecationWarning)
C:\Anaconda\lib\site-packages\scipy\lib\_util.py:35: DeprecationWarning: Module scipy.linalg.blas.fblas is deprecated, use scipy.linalg.blas instead
  DeprecationWarning)
C:\Anaconda\lib\site-packages\scipy\lib\_util.py:35: DeprecationWarning: Module scipy.linalg.blas.fblas is deprecated, use scipy.linalg.blas instead
  DeprecationWarning)
C:\Anaconda\lib\site-packages\scipy\lib\_util.py:35: DeprecationWarning: Module scipy.linalg.blas.fblas is deprecated, use scipy.linalg.blas instead
  DeprecationWarning)
C:\Anaconda\lib\site-packages\scipy\lib\_util.py:35: DeprecationWarning: Module scipy.linalg.blas.fblas is deprecated, use scipy.linalg.blas instead
  DeprecationWarning)
C:\Anaconda\lib\site-packages\scipy\lib\_util.py:35: DeprecationWarning: Module scipy.linalg.blas.fblas is deprecated, use scipy.linalg.blas instead
  DeprecationWarning)
C:\Anaconda\lib\site-packages\scipy\lib\_util.py:35: DeprecationWarning: Module scipy.linalg.blas.fblas is deprecated, use scipy.linalg.blas instead
  DeprecationWarning)
C:\Anaconda\lib\site-packages\scipy\lib\_util.py:35: DeprecationWarning: Module scipy.linalg.blas.fblas is deprecated, use scipy.linalg.blas instead
  DeprecationWarning)
Using gpu device 0: Quadro K2200 (CNMeM is disabled)
In [4]: 
datafile = '../mnist.pkl.gz'
# Load data.                                                                                                   

with gzip.open(datafile,'rb') as f:                                                                        
    train_set, val_set, test_set = cPickle.load(f)                                                       

X, Z = train_set                                                                                               
VX, VZ = val_set
TX, TZ = test_set

Z = one_hot(Z, 10)
VZ = one_hot(VZ, 10)
TZ = one_hot(TZ, 10)

X_no_bin = X
VX_no_bin = VX
TX_no_bin = TX

# binarize the MNIST data
np.random.seed(0)
X  = np.random.binomial(1, X) * 1.0
VX = np.random.binomial(1, VX) * 1.0
TX = np.random.binomial(1, TX) * 1.0

image_dims = 28, 28

X_np, Z_np, VX_np, VZ_np, TX_np, TZ_np, X_no_bin_np, VX_no_bin_np, TX_no_bin_np = X, Z, VX, VZ, TX, TZ, X_no_bin, VX_no_bin, TX_no_bin
X, Z, VX, VZ, TX, TZ, X_no_bin, VX_no_bin, TX_no_bin = [cast_array_to_local_type(i) 
                                                        for i in (X, Z, VX,VZ, TX, TZ, X_no_bin, VX_no_bin, TX_no_bin)]
print X.shape

(50000L, 784L)


\\srv-file.brml.tum.de\nthome\cwolf\code\2015-christopherwolf-msc\breze\learn\base.py:39: UserWarning: Implicilty converting numpy.ndarray to gnumpy.garray
  warnings.warn('Implicilty converting numpy.ndarray to gnumpy.garray')
In [15]: 
fig, ax = plt.subplots(figsize=(9, 9))

img = tile_raster_images(X_np[:64], image_dims, (8, 8), (1, 1))
ax.imshow(img, cmap=cm.binary)
Out[15]:
<matplotlib.image.AxesImage at 0x37b6b630>
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [9]: 
fast_dropout = False

if fast_dropout:
    class MyHmcViModel(HmcViModel, 
                   hvi.FastDropoutMlpBernoulliVisibleVAEMixin, 
                   hvi.FastDropoutMlpGaussLatentVAEMixin, 
                   DiagGaussKinEnergyMixin,
                   MlpGaussInvModelMixin):
        pass

    kwargs = {
        'p_dropout_inpt': .1,
        'p_dropout_hiddens': [.2, .2],
    }

    print 'yeah'

else:
    class MyHmcViModel(HmcViModel, 
                   hvi.MlpBernoulliVisibleVAEMixin, 
                   hvi.MlpGaussLatentVAEMixin, 
                   DiagGaussKinEnergyMixin,
                   MlpGaussInvModelMixin):
        pass
    kwargs = {}


batch_size = 200
#optimizer = 'rmsprop', {'step_rate': 1e-4, 'momentum': 0.95, 'decay': .95, 'offset': 1e-6}
#optimizer = 'adam', {'step_rate': .5, 'momentum': 0.9, 'decay': .95, 'offset': 1e-6}
optimizer = 'adam', {'step_rate': 0.001}

# This is the number of random variables NOT the size of 
# the sufficient statistics for the random variables.
n_latents = 2
n_hidden = 200

m = MyHmcViModel(X.shape[1], n_latents, 
                 [n_hidden, n_hidden], ['rectifier'] * 2, 
                 [n_hidden], ['rectifier'] * 1, 
                 [n_hidden], ['rectifier'] * 1,
                 n_hmc_steps=3, n_lf_steps=4,
                 n_z_samples=1,
          optimizer=optimizer, batch_size=batch_size, allow_partial_velocity_update=False, perform_acceptance_step=False,
          **kwargs)

#climin.initialize.randomize_normal(m.parameters.data, 0.1, 1e-1)
#m.parameters.__setitem__(m.hmc_sampler.step_size_param, 0.2)
#m.parameters.__setitem__(m.kin_energy.mlp.layers[-1].bias, 1)
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [10]: 
old_best_params = None
#print m.score(TX)
print m.parameters.data.shape

(514595,)
In [11]: 
FILENAME = 'hvi_gen2_recog1_aux1_late2_hid200_fullbin_3hmc_04lf.pkl'

# In[5]:
#old_best_params = None
f = open(FILENAME, 'rb')
np_array = cPickle.load(f)
old_best_params = cast_array_to_local_type(np_array)
f.close()
print old_best_params.shape

(514595,)
In [12]: 
m.parameters.data = old_best_params.copy()
#old_best_loss = m.score(VX)
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [13]: 
print m.score(VX)
print m.score(TX)

compiled score function
garray(146.8500518798828)
garray(148.2480010986328)
In [10]: 
print m.parameters.view(m.init_recog.mlp.layers[2].bias)

[-0.20392939  0.00867672 -3.15998387 -3.66515756]
In [60]: 
#m.parameters.__setitem__(m.hmc_sampler.step_size_param, 0.2)
#m.parameters.__setitem__(m.init_recog.mlp.layers[2].bias, np.array([-0.20392939,  0.00867672, -3.15998387, -3.66515756]).astype('float32'))
In [14]: 
print 0.1 * m.parameters.view(m.hmc_sampler.step_size_param) ** 2 + 1e-8

garray([ 0.01367096])
In [87]: 
#print m.estimate_nll(TX, 500)

142.505125
In [None]: 
print m.score(VX_no_bin)
print m.score(TX_no_bin)
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [None]: 
max_passes = 250
max_iter = max_passes * X.shape[0] / batch_size
n_report = X.shape[0] / batch_size

stop = climin.stops.AfterNIterations(max_iter)
pause = climin.stops.ModuloNIterations(n_report)

# theano.config.optimizer = 'fast_compile'

for i, info in enumerate(m.powerfit((X_no_bin,), (VX,), stop, pause, eval_train_loss=False)):
    print i, info['loss'], info['val_loss']
    if i == 0 and old_best_params is not None:
        if info['best_loss'] > old_best_loss:
            info['best_loss'] = old_best_loss
            info['best_pars'] = old_best_params
    
    if info['best_loss'] == info['val_loss']:
        np.savetxt('hvi_short_basic_test.csv', m.parameters.data, delimiter=',')
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [16]: 
f_z_init_sample = m.function(['inpt'], m.init_recog.sample())
f_z_sample = m.function(['inpt'], m.hmc_sampler.output)
f_gen = m.function([m.gen.inpt], m.gen.sample())
f_gen_rate = m.function([m.gen.inpt], m.gen.rate)

INFO (theano.gof.compilelock): Waiting for existing lock by process '3812' (I am process '3776')
INFO:theano.gof.compilelock:Waiting for existing lock by process '3812' (I am process '3776')
INFO (theano.gof.compilelock): To manually release the lock, delete C:\Users\cwolf\AppData\Local\Theano\compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_60_Stepping_3_GenuineIntel-2.7.7-64\lock_dir
INFO:theano.gof.compilelock:To manually release the lock, delete C:\Users\cwolf\AppData\Local\Theano\compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_60_Stepping_3_GenuineIntel-2.7.7-64\lock_dir
In [17]: 
curr_pos = T.matrix('current_position')
curr_vel = T.matrix('current_velocity')
norm_noise = T.matrix('normal_noise')
unif_noise = T.vector('uniform_noise')

new_sampled_vel = m.hmc_sampler.kin_energy.sample(norm_noise)
updated_vel = m.hmc_sampler.partial_vel_constant * curr_vel + m.hmc_sampler.partial_vel_complement * new_sampled_vel
performed_hmc_steps = m.hmc_sampler.perform_hmc_steps(curr_pos, curr_vel)
hmc_step = m.hmc_sampler.hmc_step(curr_pos, curr_vel, np.float32(0), norm_noise, unif_noise)
lf_step_results = m.hmc_sampler.simulate_dynamics(curr_pos, curr_vel, return_full_list=True)

f_pot_en = m.function(['inpt', curr_pos], m.hmc_sampler.eval_pot_energy(curr_pos))
f_kin_en = m.function(['inpt', curr_vel], m.kin_energy.nll(curr_vel).sum(-1))
f_perform_hmc_steps = m.function(['inpt', curr_pos, curr_vel], 
                                T.concatenate([performed_hmc_steps[0], performed_hmc_steps[1]], axis=1))
f_hmc_step = m.function(['inpt', curr_pos, curr_vel, norm_noise, unif_noise], 
                        T.concatenate([hmc_step[0], hmc_step[1]],axis=1), on_unused_input='warn')
f_kin_energy_sample_from_noise = m.function(['inpt', norm_noise], new_sampled_vel)
f_updated_vel_from_noise = m.function(['inpt', curr_vel, norm_noise], updated_vel)
f_perform_lf_steps = m.function(['inpt', curr_pos, curr_vel],
                               T.concatenate([lf_step_results[0], lf_step_results[1]], axis=0))

\\srv-file.brml.tum.de\nthome\cwolf\code\2015-christopherwolf-msc\breze\arch\util.py:583: UserWarning: theano.function was asked to create a function computing outputs given certain inputs, but the provided input variable at index 5 is not part of the computational graph needed to compute the outputs: uniform_noise-for-gpu.
To make this warning into an error, you can pass the parameter on_unused_input='raise' to theano.function. To disable it completely, use on_unused_input='ignore'.
  on_unused_input=on_unused_input, updates=updates)
In [27]: 
f_z_init_mean = m.function(['inpt'], m.init_recog.mean)
f_z_init_var = m.function(['inpt'], m.init_recog.var)

f_v_init_var = m.function(['inpt'], m.kin_energy.var)

full_sample = m.hmc_sampler.sample_with_path()
f_full_sample = m.function(['inpt'], T.concatenate([full_sample[0], full_sample[1]], axis=1))
In [19]: 
final_pos = T.matrix('final_pos')
final_vel = T.matrix('final_vel')
inpt_replacements = {m.final_vel_model_inpt['position']: final_pos,
                     m.final_vel_model_inpt['time']: T.cast(m.hmc_sampler.n_hmc_steps, dtype='float32')}

final_vel_model_var = clone(m.final_vel_model.var, replace=inpt_replacements)
final_vel_model_mean = clone(m.final_vel_model.mean, replace=inpt_replacements)
final_vel_model_nll = clone(m.final_vel_model.nll(final_vel).sum(-1), replace=inpt_replacements)

f_v_final_var = m.function(['inpt', final_pos], final_vel_model_var)
f_v_final_mean = m.function(['inpt', final_pos], final_vel_model_mean)
f_v_final_model_nll = m.function(['inpt', final_pos, final_vel], final_vel_model_nll)
In [23]: 
f_init_recog_nll = m.function(['inpt'], m.init_recog.expected_nll.sum(-1))
In [28]: 
print f_init_recog_nll(X).mean()
print f_z_init_var(X).mean()
print f_z_init_var(X).max()
print f_z_init_var(X).min()

-0.185972402344


---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-28-b9c26e22e8f3> in <module>()
      1 print f_init_recog_nll(X).mean()
----> 2 print f_z_init_var(X).mean()
      3 print f_z_init_var(X).max()
      4 print f_z_init_var(X).min()

\\srv-file.brml.tum.de\nthome\cwolf\code\2015-christopherwolf-msc\breze\arch\util.pyc in f_implicit_pars(*args, **kwargs)
    588         if not explicit_pars:
    589             def f_implicit_pars(*args, **kwargs):
--> 590                 return f(self.parameters.data, *args, **kwargs)
    591             f_implicit_pars.theano_func = f
    592             f_implicit_pars.breze_func = True

\\srv-file.brml.tum.de\nthome\cwolf\code\2015-christopherwolf-msc\breze\arch\util.pyc in inner(*args)
    186             # TODO: check for CudaNdArray instance instead
    187             if not isinstance(res, (float, np.ndarray)):
--> 188                 res = gput.cudandarray_to_garray(res)
    189         return res
    190 

\\srv-file.brml.tum.de\nthome\cwolf\code\ml_support\theano\theano\misc\gnumpy_utils.pyc in cudandarray_to_garray(x, copyif)
     56                     x = x.copy()
     57                 else:
---> 58                     raise ValueError("We where asked to don't copy memory, but the memory is not c contiguous.")
     59             # Now x is always c contiguous.
     60 

ValueError: We where asked to don't copy memory, but the memory is not c contiguous.
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [37]: 
fig, axs = plt.subplots(2, 3, figsize=(27, 18))

### Original data

O = (X_no_bin_np[:64])[:, :784].astype('float32')
img = tile_raster_images(O, image_dims, (8, 8), (1, 1))
axs[0, 0].imshow(img, cmap=cm.binary)

O2 = (X_np[:64])[:, :784].astype('float32')
img = tile_raster_images(O2, image_dims, (8, 8), (1, 1))
axs[1, 0].imshow(img, cmap=cm.binary)

### Reconstruction

#z_sample = f_z_sample((X[:64]))
z_init_sample = f_z_init_sample((X[:64]))
z_sample = f_perform_hmc_steps((X[:64]), 
                               z_init_sample, 
                               f_kin_energy_sample_from_noise((X[:64]), 
                                                              cast_array_to_local_type(np.random.normal(size=(64, m.n_latent)).astype('float32')))
                               )[-1, :64, :]

R = f_gen_rate(z_sample)[:, :784].astype('float32')
img = tile_raster_images(R, image_dims, (8, 8), (1, 1))
axs[0, 1].imshow(img, cmap=cm.binary)

Rinit = f_gen_rate(z_init_sample)[:, :784].astype('float32')
img = tile_raster_images(Rinit, image_dims, (8, 8), (1, 1))
axs[0, 2].imshow(img, cmap=cm.binary)

R2 = f_gen(z_sample)[:, :784].astype('float32')
img = tile_raster_images(R2, image_dims, (8, 8), (1, 1))
axs[1, 1].imshow(img, cmap=cm.binary)

Rinit2 = f_gen(z_init_sample)[:, :784].astype('float32')
img = tile_raster_images(Rinit2, image_dims, (8, 8), (1, 1))
axs[1, 2].imshow(img, cmap=cm.binary)
Out[37]:
<matplotlib.image.AxesImage at 0x74099ba8>
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [32]: 
fig, axs = plt.subplots(1, 2, figsize=(18, 9))

prior_sample = cast_array_to_local_type(np.random.randn(64, m.n_latent))

S = f_gen_rate(prior_sample)[:, :784].astype('float32')
img = tile_raster_images(S, image_dims, (8, 8), (1, 1))
axs[0].imshow(img, cmap=cm.binary)

S2 = f_gen(prior_sample)[:, :784].astype('float32')
img = tile_raster_images(S2, image_dims, (8, 8), (1, 1))
axs[1].imshow(img, cmap=cm.binary)

#S3 = f_gen_rate(prior_sample)[:, :784].astype('float32')
#img = tile_raster_images(S, image_dims, (8, 8), (1, 1))
#axs[2, 2].imshow(img, cmap=cm.nipy_spectral)
Out[32]:
<matplotlib.image.AxesImage at 0x2ef696d8>
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [39]: 
# TODO: Axis titles, plot title, make this work if one selects two dimensions out of more than two (i.e. if n_latent>2)

from scipy.stats import norm as normal_distribution

unit_interval_positions = np.linspace(0.025, 0.975, 20)
positions = normal_distribution.ppf(unit_interval_positions)
print unit_interval_positions
print positions

latent_array = np.zeros((400, 2))

latent_array[:, 1] = -np.repeat(positions, 20)  # because images are filled top -> bottom, left -> right (row by row)
latent_array[:, 0] = np.tile(positions, 20)
        
fig, axs = plt.subplots(1, 1, figsize=(24, 24))

F = f_gen_rate(cast_array_to_local_type(latent_array)).astype('float32')

img = tile_raster_images(F, image_dims, (20, 20), (1, 1))
#axs.imshow(img, cmap=cm.nipy_spectral)
axs.imshow(img, cmap=cm.binary)

[ 0.025  0.075  0.125  0.175  0.225  0.275  0.325  0.375  0.425  0.475
  0.525  0.575  0.625  0.675  0.725  0.775  0.825  0.875  0.925  0.975]
[-1.95996398 -1.43953147 -1.15034938 -0.93458929 -0.75541503 -0.59776013
 -0.45376219 -0.31863936 -0.18911843 -0.06270678  0.06270678  0.18911843
  0.31863936  0.45376219  0.59776013  0.75541503  0.93458929  1.15034938
  1.43953147  1.95996398]
Out[39]:
<matplotlib.image.AxesImage at 0x789e5588>
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [44]: 
L = f_z_sample(X).astype('float32')
L_init = f_z_init_sample(X).astype('float32')
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [45]: 
dim1 = 0
dim2 = 1
In [46]: 
fig, axs = plt.subplots(1, 2, figsize=(18, 9))
axs[0].scatter(L[:, dim1], L[:, dim2], c=Z[:].argmax(1), lw=0, s=5, alpha=.2)
axs[1].scatter(L_init[:, dim1], L_init[:, dim2], c=Z[:].argmax(1), lw=0, s=5, alpha=.2)

cax = fig.add_axes([0.95, 0.2, 0.02, 0.6])
cax.scatter(np.repeat(0, 10), np.arange(10), c=np.arange(10), lw=0, s=300)
cax.set_xlim(-0.1, 0.1)
cax.set_ylim(-0.5, 9.5)
plt.yticks(np.arange(10))
plt.tick_params(axis='x', which='both', bottom='off', top='off', labelbottom='off')
cax.tick_params(axis='y', colors='white')
for tick in cax.yaxis.get_major_ticks():
    tick.label.set_fontsize(14)
    tick.label.set_color('black')
    
cax.spines['bottom'].set_color('white')
cax.spines['top'].set_color('white') 
cax.spines['right'].set_color('white')
cax.spines['left'].set_color('white')

axs[0].set_title('After HMC steps')
axs[1].set_title('Initial recognition model')

axs[0].set_xlim(-3, 3)
axs[0].set_ylim(-3, 3)
axs[1].set_xlim(-3, 3)
axs[1].set_ylim(-3, 3)
Out[46]:
(-3, 3)
In [47]: 
fig, axs = plt.subplots(4, 5, figsize=(20, 16))
colors = cm.jet(np.linspace(0, 1, 10))
for i in range(5):
    axs[0, i].scatter(L_init[Z[:].argmax(1) == i, dim1], L_init[Z[:].argmax(1) == i, dim2], c=colors[i], lw=0, s=5, alpha=.2)
    axs[1, i].scatter(L[Z[:].argmax(1) == i, dim1], L[Z[:].argmax(1) == i, dim2], c=colors[i], lw=0, s=5, alpha=.2)
    axs[0, i].set_title(str(i) + ' before HMC')
    axs[1, i].set_title(str(i) + ' after HMC')
    axs[2, i].scatter(L_init[Z[:].argmax(1) == (5+i), dim1], L_init[Z[:].argmax(1) == (5+i), dim2], c=colors[5+i], lw=0, s=5, alpha=.2)
    axs[3, i].scatter(L[Z[:].argmax(1) == (5+i), dim1], L[Z[:].argmax(1) == (5+i), dim2], c=colors[5+i], lw=0, s=5, alpha=.2)
    axs[2, i].set_title(str(5+i) + ' before HMC')
    axs[3, i].set_title(str(5+i) + ' after HMC')
    for j in range(4):
        axs[j, i].set_xlim(-3, 3)
        axs[j, i].set_ylim(-3, 3)
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [48]: 
X_index = 24  # index=0 -> 5, index=1 -> 0, index=2 -> 4, index=3 -> 1, index=24 -> underlined 1, index=39 -> ugly 6
num_repeats = 1000

fig, axs = plt.subplots(1, 2, figsize=(6, 3))
img = tile_raster_images(np.array([X[X_index, :]]), image_dims, (1, 1), (1, 1))
axs[0].imshow(img, cmap=cm.binary)
img = tile_raster_images(np.array([X_no_bin[X_index, :]]), image_dims, (1, 1), (1, 1))
axs[1].imshow(img, cmap=cm.binary)
Out[48]:
<matplotlib.image.AxesImage at 0x2c4efb38>
In [54]: 
repeated_X = np.tile(np.array([X[X_index, :]]), (num_repeats, 1)).astype('float32')

full_sample = f_full_sample(cast_array_to_local_type(repeated_X)).astype('float32')
z_samples = full_sample[:, :num_repeats, :]
v_samples = full_sample[:, num_repeats:, :]

z_sample_final_mean = z_samples[m.n_hmc_steps, :, :].mean(axis=0)
z_sample_final_std = z_samples[m.n_hmc_steps, :, :].std(axis=0)

single_X = cast_array_to_local_type(np.array([X[X_index, :]]).astype('float32'))
init_mean = f_z_init_mean(single_X)[0]
init_var = f_z_init_var(single_X)[0]

init_vel_var = f_v_init_var(single_X)[0]

print 'Posterior distribution statistics'
print
print 'Initial model: - Mean: ' + str(init_mean)
print '               - Var:  ' + str(init_var)
print
print 'Full HVI model: - Mean: ' + str(z_sample_final_mean)
print '                - Var:  ' + str(z_sample_final_std ** 2)
print
print 'Velocity model variance: ' + str(init_vel_var)

Posterior distribution statistics

Initial model: - Mean: garray([ 0.02788965,  0.34757963])
               - Var:  garray([ 0.24179861,  0.25031441])

Full HVI model: - Mean: [-0.01340033  0.37820706]
                - Var:  [ 0.2420868  0.2175556]

Velocity model variance: garray([ 0.79692739,  0.6917206 ])
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [29]: 
dim1 = 0
dim2 = 1
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [77]: 
resolution = 201
lower_dim1_limit = z_sample_final_mean[dim1] - 0.2
upper_dim1_limit = z_sample_final_mean[dim1] + 0.2
lower_dim2_limit = z_sample_final_mean[dim2] - 0.2
upper_dim2_limit = z_sample_final_mean[dim2] + 0.2

number_images_per_axis = 11
latent_array = np.zeros((number_images_per_axis**2, 2))
gap_between_images = (resolution - 1)//(number_images_per_axis - 1)
indices_for_images = np.arange(0, resolution, gap_between_images)

pot_energy_matrix = np.zeros((resolution, resolution), dtype='float32')
x = cast_array_to_local_type(np.linspace(lower_dim1_limit, upper_dim1_limit, resolution))
y = cast_array_to_local_type(np.linspace(lower_dim2_limit, upper_dim2_limit, resolution))
for i in range(resolution):
    for j in range(resolution):
        #pos_array = f_z_init_mean(np.array([X[X_index, :]]))
        pos_array = np.array([z_sample_final_mean])
        pos_array[0, dim1] = x[i]
        pos_array[0, dim2] = y[j]
        pot_energy_matrix[j, i] = f_pot_en(np.array([X[X_index, :]]), pos_array)
        if i in indices_for_images and j in indices_for_images:
            latent_array[(i//gap_between_images) + (number_images_per_axis - 1 - j//gap_between_images)*number_images_per_axis , :] = pos_array[0, :]

        
print 'Minimum potential energy (at grid points): ' + str(pot_energy_matrix.min())
print 'Maximum potential energy (at grid points): ' + str(pot_energy_matrix.max())

fig, axs = plt.subplots(1, 2, figsize=(18, 9))
CS = axs[0].contour(x, y, pot_energy_matrix, 20)
plt.clabel(CS, inline=1, fmt='%1.0f', fontsize=10)
axs[0].set_title('Potential energy surface')

F = f_gen_rate(latent_array.astype('float32'))
img = tile_raster_images(F, image_dims, (number_images_per_axis, number_images_per_axis), (1, 1))
#axs.imshow(img, cmap=cm.nipy_spectral)
axs[1].imshow(img, cmap=cm.binary)
plt.show()

Minimum potential energy (at grid points): 169.46
Maximum potential energy (at grid points): 283.837
In [79]: 
resolution = 200
underlying_variance = f_v_init_var(np.array([X[X_index, :]]))
velocity_range_for_images = 10.0 * np.sqrt(underlying_variance[0, :])
lower_dim1_limit = np.around(- velocity_range_for_images[dim1])
upper_dim1_limit = np.around(  velocity_range_for_images[dim1])
lower_dim2_limit = np.around(- velocity_range_for_images[dim2])
upper_dim2_limit = np.around(  velocity_range_for_images[dim2])

kin_energy_matrix = np.zeros((resolution, resolution), dtype='float32')
kin_x = cast_array_to_local_type(np.linspace(lower_dim1_limit, upper_dim1_limit, resolution))
kin_y = cast_array_to_local_type(np.linspace(lower_dim2_limit, upper_dim2_limit, resolution))
for i in range(resolution):
    for j in range(resolution):
        vel_array = np.zeros((1, m.n_latent)).astype('float32')
        vel_array[0, dim1] = kin_x[i]
        vel_array[0, dim2] = kin_y[j]
        kin_energy_matrix[j, i] = f_kin_en(np.array([X[X_index, :]]), vel_array)

print 'Minimum kinetic energy (at grid points): ' + str(kin_energy_matrix.min())
print 'Maximum kinetic energy (at grid points): ' + str(kin_energy_matrix.max())

fig, ax = plt.subplots(1, 1, figsize=(9, 9))
CS = ax.contour(kin_x, kin_y, kin_energy_matrix)
plt.clabel(CS, inline=1, fmt='%1.1f', fontsize=10)
ax.set_title('Kinetic energy surface')
plt.show()

Minimum kinetic energy (at grid points): 1.83479
Maximum kinetic energy (at grid points): 102.397
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [80]: 
fig, axs = plt.subplots(m.n_hmc_steps + 1, 3, figsize=(18, (m.n_hmc_steps + 1) * 6))
colors = cm.jet(np.linspace(0, 1, 10))

#contour_levels = (198, 200, 202, 204, 206, 208, 210)
#contour_levels = (130, 140, 150, 160, 180, 200, 240, 280)
#contour_levels = (180, 190, 200, 220, 240, 260, 280, 300, 320)
#contour_levels = (400, 402, 404, 406, 408, 410, 412, 416, 420)
#contour_levels = (106, 108, 110, 112, 114, 116, 118, 120, 124, 128)
contour_levels = (160, 165, 170, 175, 180, 185, 190, 195, 200, 210, 220, 230, 240, 250, 270, 300)
#contour_levels = (174, 175, 176, 177, 178, 180, 182, 184, 186, 190, 200)
#contour_levels = (59, 61, 63, 65, 67, 69, 71, 73, 75, 80, 85, 90)

vel_contour_levels = np.linspace(2.0, 70.0, 18)
#CS0 = axs[0, 0].contourf(x, y, pot_energy_matrix, np.linspace(155, 240, 500))

def colour_for_z_samples(samples):
    mean = samples.mean(axis=0)
    mean1 = mean[dim1]
    mean2 = mean[dim2]
    colour = np.zeros_like(samples[:, 0])
    colour[np.logical_and(samples[:, dim1] < mean1,  samples[:, dim2] < mean2)] = 0
    colour[np.logical_and(samples[:, dim1] < mean1,  samples[:, dim2] >= mean2)] = 2
    colour[np.logical_and(samples[:, dim1] >= mean1, samples[:, dim2] < mean2)] = 4
    colour[np.logical_and(samples[:, dim1] >= mean1, samples[:, dim2] >= mean2)] = 7
    colour[((samples[:, dim1] - mean1) ** 2 + (samples[:, dim2] - mean2) ** 2) < 1e-5] = 9
    return colour.astype('int32')

colour = colour_for_z_samples(z_samples[m.n_hmc_steps,:,:])
print v_samples[m.n_hmc_steps, colour == 0, :].mean(axis=0)
print v_samples[m.n_hmc_steps, colour == 2, :].mean(axis=0)
print v_samples[m.n_hmc_steps, colour == 4, :].mean(axis=0)
print v_samples[m.n_hmc_steps, colour == 7, :].mean(axis=0)
print v_samples[m.n_hmc_steps, colour == 9, :].mean(axis=0)
print v_samples[m.n_hmc_steps, colour == 0, :].var(axis=0)
print v_samples[m.n_hmc_steps, colour == 2, :].var(axis=0)
print v_samples[m.n_hmc_steps, colour == 4, :].var(axis=0)
print v_samples[m.n_hmc_steps, colour == 7, :].var(axis=0)
print v_samples[m.n_hmc_steps, colour == 9, :].var(axis=0)

for i in range(m.n_hmc_steps + 1):
    CS = axs[i, 0].contour(x, y, pot_energy_matrix, contour_levels)
    plt.clabel(CS, inline=1, fmt='%1.0f', fontsize=10)
    axs[i, 0].scatter(z_samples[i,:,dim1], z_samples[i,:,dim2], c=colors[colour_for_z_samples(z_samples[i,:,:])], s=20, alpha=.3, lw=0)
    
    CS_vel = axs[i, 1].contour(kin_x, kin_y, kin_energy_matrix, vel_contour_levels)
    plt.clabel(CS_vel, inline=1, fmt='%1.1f', fontsize=10)
    axs[i, 1].scatter(v_samples[i,:,dim1], v_samples[i,:,dim2], c=colors[colour_for_z_samples(z_samples[i,:,:])], s=20, alpha=.3, lw=0)
    
    pot_energy_distrib = f_pot_en(repeated_X, z_samples[i, :, :])
    if i == 0:
        max_x_value_for_hist = pot_energy_distrib.max() + 5
        min_x_value_for_hist = np.floor(pot_energy_matrix.min()) -5
    pot_energy_distrib_mean = pot_energy_distrib.mean()
    axs[i, 2].hist(pot_energy_distrib, 30, normed=1, range=(min_x_value_for_hist, max_x_value_for_hist))
    axs[i, 2].autoscale(enable=False, axis='both')
    axs[i, 2].axvline(pot_energy_distrib_mean, color='r', linestyle='dashed', linewidth=2)
    axs[i, 2].set_xlim(min_x_value_for_hist, max_x_value_for_hist)
    axs[i, 2].text(pot_energy_distrib_mean + 1.0, 0.8*axs[i, 2].get_ylim()[1], 'Mean: ' + str(pot_energy_distrib_mean))
    axs[i, 1].set_xlim(-velocity_range_for_images[dim1], velocity_range_for_images[dim1])
    axs[i, 1].set_ylim(-velocity_range_for_images[dim2], velocity_range_for_images[dim2])

axs[0, 0].scatter(f_z_init_mean(np.array([X[X_index,:]]))[0, dim1], f_z_init_mean(np.array([X[X_index,:]]))[0, dim2], c='black', s=20)

plt.show()

[ 1.46786869  0.1229062 ]
[ 1.52937722  0.46723852]
[ 1.57169867  0.07256739]
[ 1.36901832  0.20566869]
[ 1.72286248  0.26369664]
[ 2.57220793  1.51032341]
[ 1.83856583  1.48337376]
[ 1.3634491   1.45219004]
[ 1.20035243  0.92484128]
[ 1.20959449  1.55986774]
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [83]: 
np.random.seed(1)

velocity_noise = np.random.normal(size=(m.n_hmc_steps, 1, m.n_latent)).astype('float32')
#velocity_noise = np.zeros_like(velocity_noise)
single_X = np.array([X[X_index, :]])

init_pos = f_z_init_mean(single_X)
init_vel = f_kin_energy_sample_from_noise(single_X, velocity_noise[0])

num_vels_per_hmc = (m.n_lf_steps + 2)
position_array = np.zeros((m.n_hmc_steps * m.n_lf_steps + 1, m.n_latent))
position_array[0] = init_pos
velocity_array = np.zeros((m.n_hmc_steps * num_vels_per_hmc, m.n_latent))
velocity_array[0] = init_vel

for hmc_num in range(m.n_hmc_steps):
    if hmc_num == 0:
        curr_pos = init_pos
        curr_vel = init_vel
    else:
        curr_vel = f_updated_vel_from_noise(single_X, curr_vel, velocity_noise[hmc_num])
        velocity_array[hmc_num * (m.n_lf_steps + 2)] = curr_vel
    
    lf_step_results = f_perform_lf_steps(single_X, curr_pos, curr_vel)
    pos_steps = lf_step_results[:m.n_lf_steps]
    vel_half_steps_and_final = lf_step_results[m.n_lf_steps:]
    final_vel = lf_step_results[-1]
    final_pos = pos_steps[-1]
    
    position_array[hmc_num * m.n_lf_steps + 1: (hmc_num + 1)*m.n_lf_steps + 1] = pos_steps[:, 0, :]
    velocity_array[hmc_num * num_vels_per_hmc + 1: (hmc_num + 1) * num_vels_per_hmc] = vel_half_steps_and_final[:, 0, :]
    
    curr_pos = final_pos
    curr_vel = final_vel
In [84]: 
fig, axs = plt.subplots(1, 2, figsize=(18, 9))
step_color = cm.jet(np.linspace(0, 1, position_array.shape[0]))
CS = axs[0].contour(x, y, pot_energy_matrix, contour_levels)
CS_vel = axs[1].contour(kin_x, kin_y, kin_energy_matrix, vel_contour_levels)
hmc_step_indices = np.arange(0, position_array.shape[0], m.n_lf_steps)
size_array = 40*np.ones((position_array.shape[0],))
size_array[hmc_step_indices] = 100
axs[0].scatter(position_array[:, dim1], position_array[:, dim2], c=step_color, lw=1, s=size_array)
axs[1].set_color_cycle(step_color)

for hmc_num in range(m.n_hmc_steps):
    curr_vel_range = np.arange(num_vels_per_hmc * hmc_num, num_vels_per_hmc * (hmc_num + 1) - 2)
    init_vel_ind = hmc_num * num_vels_per_hmc
    final_vel_ind = (hmc_num + 1) * num_vels_per_hmc - 1
    curr_index = hmc_step_indices[hmc_num]
    next_index = hmc_step_indices[hmc_num + 1]
    for j in curr_vel_range:
        axs[1].plot(velocity_array[j:j+2, dim1], velocity_array[j:j+2, dim2], lw=2)
    axs[1].scatter(velocity_array[init_vel_ind, dim1], velocity_array[init_vel_ind, dim2], c=step_color[curr_index], lw=0, s=100)
    axs[1].scatter(velocity_array[final_vel_ind, dim1], velocity_array[final_vel_ind, dim2], c=step_color[next_index], lw=0, s=100)

for hmc_num in range(m.n_hmc_steps):
    final_vel_ind = (hmc_num + 1) * num_vels_per_hmc - 1
    next_index = hmc_step_indices[hmc_num + 1]
    axs[1].plot(velocity_array[final_vel_ind-1:final_vel_ind+1, dim1], velocity_array[final_vel_ind-1:final_vel_ind+1, dim2], lw=2, c=step_color[next_index])
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [None]: 
variation_start = z_sample_final_mean - 2*z_sample_final_std
variation_end = z_sample_final_mean + 2*z_sample_final_std

final_vel_model_mean_output = np.zeros((m.n_latent, num_repeats, m.n_latent))
final_vel_model_var_output = np.zeros((m.n_latent, num_repeats, m.n_latent))

for variation_dim in range(m.n_latent):
    z_variation = np.linspace(variation_start[variation_dim], variation_end[variation_dim], num_repeats)
    sample_array = np.tile(z_sample_final_mean, (num_repeats, 1))
    sample_array[:, variation_dim] = z_variation
    final_vel_model_mean_output[variation_dim] = f_v_final_mean(repeated_X, sample_array)
    final_vel_model_var_output[variation_dim] = f_v_final_var(repeated_X, sample_array)
In [None]: 
fig, axs = plt.subplots(1, 2, figsize=(18, 9))
axs[0].scatter(final_vel_model_mean_output[:, :, dim1], 
           final_vel_model_mean_output[:, :, dim2],  
           c=np.transpose(np.tile(np.linspace(0,m.n_latent-1,m.n_latent), (num_repeats, 1))), 
           lw=0, s=5)
axs[1].scatter(final_vel_model_var_output[:, :, dim1], 
           final_vel_model_var_output[:, :, dim2],  
           c=np.transpose(np.tile(np.linspace(0,m.n_latent-1,m.n_latent), (num_repeats, 1))), 
           lw=0, s=5)

plt.show()
In [None]: 
final_vel_mean = f_v_final_mean(repeated_X, z_samples[3, :, :])
final_vel_var = f_v_final_var(repeated_X, z_samples[3, :, :])
final_vel_nll = f_v_final_model_nll(repeated_X, z_samples[3, :, :], v_samples[3, :, :])
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [None]: 
fig, axs = plt.subplots(4, 2, figsize=(18, 36))
# TODO: Analysis of how final_vel_mean and final_vel_var depend on z (since they all share the same x)

print z_samples[3, :, :].mean(axis=0)
print z_samples[3, :, :].var(axis=0)
print v_samples[3, :, :].mean(axis=0)
print v_samples[3, :, :].var(axis=0)
print f_v_init_var(np.array([X[X_index, :]]))

print final_vel_nll.mean()
plt.boxplot(final_vel_nll, whis=1)
plt.show()
In [None]: 
centers = np.zeros((10,n_latents))
stddevs = np.zeros((10,n_latents))
centers_init = np.zeros((10,n_latents))
stddevs_init = np.zeros((10,n_latents))
for i in range(10):
    Li = f_z_sample(X[Z.argmax(1) == i])
    centers[i] = Li.mean(axis=0)
    stddevs[i] = np.std(Li, axis=0)
    
    Li_init = f_z_init_sample(X[Z.argmax(1) == i])
    centers_init[i] = Li_init.mean(axis=0)
    stddevs_init[i] = np.std(Li_init, axis=0)
In [None]: 
fig, axs = plt.subplots(1, 2, figsize=(18, 9))
axs[0].scatter(centers[:, dim1], centers[:, dim2], c=range(10), s=50)
axs[0].scatter(centers_init[:, dim1], centers_init[:, dim2], c=range(10), s=50, marker=u's')

axs[1].scatter(centers[:, dim1], centers[:, dim2], c=range(10), s=50)
axs[1].scatter(centers[:, dim1] + stddevs[:, dim1], centers[:, dim2], c=range(10), s=50, marker=u'>')
axs[1].scatter(centers[:, dim1] - stddevs[:, dim1], centers[:, dim2], c=range(10), s=50, marker=u'<')
axs[1].scatter(centers[:, dim1], centers[:, dim2] + stddevs[:, dim2], c=range(10), s=50, marker=u'^')
axs[1].scatter(centers[:, dim1], centers[:, dim2] - stddevs[:, dim2], c=range(10), s=50, marker=u'v')

#axs[0].set_xlim(-1.2, 1.2)
#axs[0].set_ylim(-1.2, 1.2)
#axs[1].set_xlim(-1.2, 1.2)
#axs[1].set_ylim(-1.2, 1.2)

print (centers[:, dim1] - centers_init[:, dim1])
print (centers[:, dim2] - centers_init[:, dim2])
print (stddevs[:, dim1] - stddevs_init[:, dim1])
print (stddevs[:, dim2] - stddevs_init[:, dim2])
In [None]: